Nonsymmetrized Hyperspherical Harmonics Research Articles

Beryllium-9 in cluster effective field theory

We study the ^99Be ground-state energy with non-local \alpha nαn and \alpha \alphaαα potentials derived from Cluster Effective Field Theory. The short-distance dependence of the interaction is regulated with a momentum cutoff. The potential parameters are fitted to reproduce the scattering length and effective range. We implement such potential models in a Non-Symmetrized Hyperspherical Harmonics (NSHH) code in momentum space. In addition we calculate ground-state energies of various alpha nuclei. Work is in progress on a calculation of the photodisintegration of ^99Be with the Lorentz Integral Transform (LIT) method.

Non-symmetrized Hyperspherical Harmonics Method for Non-equal Mass Three-Body Systems

The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the $^3$H, $^3$He nuclei and $^3_{\Lambda}$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and $NN\Lambda$ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between $^3$H and $^3$He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the $^3_{\Lambda}$H hypernucleus binding energy is calculated using different $NN$ and $\Lambda N$ potential models. The results have been compared with those present in the literature, finding a very nice agreement.

Benchmark Results for Few-Body Hypernuclei

The Non-Symmetrized Hyperspherical Harmonics method (NSHH) is introduced in the hypernuclear sector and benchmarked with three different ab-initio methods, namely the Auxiliary Field Diffusion Monte Carlo method, the Faddeev-Yakubovsky approach and the Gaussian Expansion Method. Binding energies and hyperon separation energies of three- to five-body hypernuclei are calculated by employing the two-body $\Lambda$N component of the phenomenological Bodmer-Usmani potential, and a hyperon-nucleon interaction simulating the scattering phase shifts given by NSC97f. The range of applicability of the NSHH method is briefly discussed.

Non-Symmetrized Hyperspherical Harmonics Method Applied to Light Hypernuclei

The present work is conducted in the field of few-body methods and it concerns the extension of the Non-Symmetrized Hyperspherical Harmonics method in order to treat quantum systems with different species of particles and additional degrees of freedom, like particle mixing. The aim is to introduce it as a new tool in the ab-initio study of light hypernuclei, and, more in general, of few-body quantum systems composed by a variety of different objects. To this end precise benchmark results for light hypernuclei with A=3-5 are provided and the perspectives of applications to systems with A>5 and the employment of the most recent hypernuclear interactions are discussed.

Ab initio calculations with non-symmetrized hyperspherical harmonics for realistic NN potential models

This contribution deals with the problem of implementing the Pauli principle in a variational calculation of the binding energy of a fermionic system on the hyperspherical harmonics (HH) basis. We summarize the main points of a method that avoids the antysimmetrization of the basis functions. In fact this gets increasingly cumbersome as the number of particles increases. The method is tested on the binding energies of two nuclei ( 4 He and 6 Li), using various nuclear potential models, including a realistic one.

Nonsymmetrized Hyperspherical Harmonics with Realistic Potentials

The Schrodinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is based on the formalism developed by Gattobigio et al. (Phys Rev A 79:032513, 2009; Few-Body Syst 45:127, 2009; Phys Rev C 83:024001, 2011), where it was applied to four- and six-body systems using central and central spin dependent potentials. In addition we include isospin dependence and noncentral forces in order to be able to make calculations also with more realistic NN potential models. Furthermore, a more efficient procedure to determine the fermionic spectrum is used. The approach is applied to four- and six-body nuclei (4He,6Li) with various NN potential models including for 4He the realistic AV18 potential. It is shown that the results for ground-state energy and radius agree well with those from the literature.

Nonsymmetrized Hyperspherical Harmonics with Realistic NN Potentials

The Schrödinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is based on the formalism developed by Gattobigio et al. (Phys Rev A 79:032513, 2009; Few-Body Syst 45:127, 2009; Phys Rev C 83:024001, 2011), where it was applied to four- and six-body systems using central and central spin dependent potentials. In addition we include isospin dependence and noncentral forces in order to be able to make calculations also with more realistic NN potential models. Furthermore, a more efficient procedure to determine the fermionic spectrum is used. The approach is applied to four- and six-body nuclei (4He,6Li) with various NN potential models including for 4He the realistic AV18 potential. It is shown that the results for ground-state energy and radius agree well with those from the literature.